In this paper Vigeland shows how one can define a group law on subset of a tropical elliptic curve, so that this group is homeomorphic to $S^1$. It is not clear to me what is the relationship between ...

In Allermann-Rau '09, the authors define the Chow groups of an arbitrary abstract tropical cycle. In particular, one may take the tropical cycle to be the tropicalization of a subvariety of a torus. ...

Edit: I realize the mathematics below is lacking a precise phrasing. I hope that the intuitiion behind the question is clear enough that a reader will understand the question and provide guidance. The ...

My excuses in advance in case my question is too vague (which is mainly due to the fact that I'm not really familiar with tropical/toric geometry, but at least I still believe that the content of the ...

I'm a beginner in tropical geometry, and I'm running into the following question:
In the usual polynomial ring over a field, one has algorithms (i.e. using a Groebner basis) for determining whether ...

Hello,
in G. Mikhalkin's Papaer "DECOMPOSITION INTO PAIRS-OF-PANTS FOR
COMPLEX ALGEBRAIC HYPERSURFACES":
http://arxiv.org/pdf/math/0205011.pdf
There is a lemma about the relation between intersection ...

I'm interested in learning tropical geometry. But my background in algebraic geometry is limited. I know basic facts about varieties in affine and projective space, but nothing about sheaves, schemes ...

Tropical geometry can be described as "algebraic geometry" over the semifield $\mathbb{T}$ of tropical numbers. As a set, $\mathbb{T}=\mathbb{R}\cup \{ -\infty\}$; this is endowed with addition being ...

In Mikhalkin's unfinished draft book on tropical geometry, (available here) (page 26) he defines a notion of tropical schemes. It seems to me that this definition is not just a wholesale adaptation of ...

Let $K$ be an algebraically closed field and $K[\underline{x}]$ its ring of polynomials in $n$ variables $x_1,\cdots, x_n$. Let $J\leq K[\underline{x}]$ be an ideal such that there are no monomials in ...

A plane tropical curve $\Gamma$ is the corner locus of a tropical polynomial in two variables. That is, it is the set of points at which the tropical polynomial, which is a piecewise-linear concave ...